density of air lb/ft3

Angle B is an acute angle in a right triangle, it must be less than 90 degrees. Therefore, a reasonable approximation for angle B ≈ 76 degrees.

In mathematics, a function is a relation between two sets of values, where each input value from the first set (called the domain) corresponds to exactly one output value in the second set (called the range). The output value of a function is determined by its input value and any relevant rules or formulas.

Formally, a function can be defined as follows: Let X and Y be two non-empty sets. A function f from X to Y is a rule or formula that assigns to each element x in X a unique element y in Y, denoted by f(x), such that for any two elements x1 and x2 in X, if x1 = x2, then f(x1) = f(x2). The set X is called the domain of the function, and the set Y is called the codomain or range of the function.

Functions can be represented graphically, algebraically, or in tabular form. The graph of a function shows how the output value of the function varies with the input value, and can be used to visualize the behavior of the function. The algebraic representation of a function can be given by a formula or equation that expresses the output value in terms of the input value. A tabular representation of a function shows the input-output pairs in a table.

Functions are used in many areas of mathematics, science, engineering, and economics to model and describe relationships between variables. They are also used in practical applications, such as in computer programming, where they are used to define algorithms and data structures.

Let's use the trigonometric ratio for the sine of angle B, which is the ratio of the opposite leg to the hypotenuse:

sin(B) = opposite leg / hypotenuse

We are given that the ratio of the opposite leg to the hypotenuse is 0.96:

opposite leg / hypotenuse = 0.96

So, we can substitute 0.96 for opposite leg / hypotenuse:

sin(B) = 0.96

Now we can use the inverse sine function to find the value of angle B:

B = sin^(-1)(0.96)

Using a calculator, we get:

B ≈ 75.96 degrees

Since angle B is an acute angle in a right triangle, it must be less than 90 degrees. Therefore, a reasonable approximation for angle B is:

B ≈ 76 degrees

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The value of x in the figure is 5

From the question, we have the following parameters that can be used in our computation:

The double triangles

On the figure, we have

RN = NP

This means that

12x = 60

Divide by 12

12x/12 = 60/12

Simplifying the left side by canceling out the 12s, we get:

x = 5

Hence, the solution to the value of x is x = 5.

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The directrix of the parabola defined by the equation (x+9)²= -16(y-5) is x=-16(y-5)+9.

Equation is a physical and mathematical statement that describe physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variables may be pointed such as you energy.

The directrix of a parabola is the line which is perpendicular to the axis of symmetry and is equidistant from the focus of the parabola. In this case, the axis of symmetry is y=5 and the focus is (9,-16).

The equation of a line perpendicular to the axis of symmetry is y=mx+b where m is the slope of the line and b is the y-intercept. The slope of the line perpendicular to the axis of symmetry is given by the negative reciprocal of the slope of the axis of symmetry. The slope of the axis of symmetry is 0, so the slope of the perpendicular line is undefined.

Using the point-slope form of the equation of a line, we can represent the equation of the directrix as x=-16(y-5)+9. This is because the point (9,-16) is equidistant from the directrix, so the y-intercept of the directrix is -16(5-5)+9 = 9.

Therefore, the directrix of the parabola defined by the equation (x+9)² = -16(y-5) is x=-16(y-5)+9.

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The complementary angles will be 65.6° and 24.4°.

What exactly are complementary angles?

Supplementary and complementary angles are defined by the sum of two angles. If the total of two angles is 90 degrees, they are considered to be complimentary angles since they produce a right angle when combined. If the total of two angles is 180 degrees, they are considered to be supplementary angles since they produce a linear angle when combined.

Now,

Let x be a angle then its complementary angle will be 90°-x as sum of complementary angles is equal to 90°.

as given

90°-x-x=18.8°

9--2x=18.8

2x=71.2

x=65.6° and 90-x°=24.4°

hence,

                The complementary angles will be 65.6° and 24.4°.

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The value of 19 in Roman numerals is XIX

Roman numerals are defined as a numeral system which originated in ancient Rome and still remains the usual way of writing numbers throughout Europe into the Late Middle Ages.

Some examples of these numeral are;

We have to represent 19, we have;

X representing ten

IX representing nine

Put them together

19 is equal to XIX

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Answer: 0.1875

Step-by-step explanation: ..

The algebraic expression for the total weight of x bags of fertilizer when each bag weighs 50 pounds is:

50x

In this expression, 50 represents the weight of each bag of fertilizer, and x represents the number of bags. When we multiply the weight of each bag by the number of bags, we get the total weight of all the bags of fertilizer.

Answer: 13

Step-by-step explanation:

the Price of each rose will be $6.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given,  Masha buys three roses she will have 7 dollars left.

Let's assume the cost of one rose is "x" dollars.

From the first piece of information, we know that if Masha buys three roses, she will have 7 dollars left.

This can be expressed as:

3x + 7 = Masha's initial amount of money

From the second piece of information, we know that Masha needs to borrow 11 dollars to buy nine roses.

This means that the cost of nine roses is:

9x - 11 = Masha's initial amount of money

Since we know that both expressions represent Masha's initial amount of money, we can set them equal to each other:

3x + 7 = 9x - 11

Subtracting 3x from both sides, we get:

7 = 6x - 11

6x = 18

x =3

Therefore, the Price of each rose will be $6.

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Answer: An increase in demand or a reduction in supply will increase the equilibrium wage. A reduction in demand or an increase in supply will reduce the equilibrium wage.

Step-by-step explanation:

Wages in a competitive market are determined by demand and supply. An increase in demand or a reduction in supply will increase the equilibrium wage. A reduction in demand or an increase in supply will reduce the equilibrium wage.

Answer:

Therefore, when  we put x=1 and y=2, the equation 3(x+2y)-2x+10 simplifies to 23.

Step-by-step explanation:

To evaluate and simplify the expression first we have to put x=1 and y=2 in the equation as given in the question,

3(x+2y)-2x+10 = 3(1+2(2))-2(1)+10

                       =3(1+2(2))-2+10

                       = 3(1+4)+8

                       = 3(5)+8

                       = 15+8

                       = 23

Therefore, when  we put x=1 and y=2, the equation 3(x+2y)-2x+10 simplifies to 23.

Answer:

6x² + 41x + 48

Step-by-step explanation:

Area (A) = l × w

Therefore,

A = (3x + 16)(2x + 3) (distribute)

A = 6x² + 9x + 32x + 48 (combine like terms)

A = 6x² + 41x + 48

Therefore, the area of the playground is 6x² + 41x + 48.

Answer: 40

Step-by-step explanation:

20% = 0.2

0.2 x 200 = 40

Table A is representing  a function, and Table B does not represent a function.

What is function?

Function, can be stated as an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

When a Table needs to be a function, it need to satisfy following conditions (look at the .jpeg image attached with this answer):

1. condition: every image has its pre-image,

in other words, In first circle, EVERY element has to be connected with SOME of the elements in second circle

2. condition: every image has only on pre-image.

in other words, In first circle, there MUSTN'T be an element that has MORE THAN ONE connection with elements in second circle

Table A satisfies BOTH of these conditions; that is why table A is indeed a function.

Table B satisfies FIRST condition but it does not satisfy the SECOND condition, that is why it is NOT a function.

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Therefore, the value of x is 26.

in geometry, an angle is a measure of the amount of rotation between two intersecting lines, or between a line and a plane. It is typically measured in degrees, with a full rotation equal to 360 degrees. Angles can also be measured in radians, which is another unit of angular measurement .Since ∠1 and ∠2 are supplementary, their sum is equal to 180 degrees. That is:

m∠1 + m∠2 = 180

Substituting the given values, we have:

124° + (2x+4)° = 180°

Simplifying this equation, we get:

2x + 128 = 180

Subtracting 128 from both sides, we have:

2x = 52

Dividing both sides by 2, we get:

x = 26

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Answer:

good for you

Step-by-step explanation:

:)

Answer;

the only LLLLLLLLLLLLLLLLLLOSERRRRRRRRRRRRRRRRRRRRRRRRRRRRR is you

Step-by-step explanation:

The equivalent expression to (2² x 3^4)^3 is given as follows:

2^6 x 3^12.

(first option).

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

Hence the exponents for this problem are given as follows:

And the simplified expression is of:

2^6 x 3^12.

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If a cylinder is sliced parallel to its base. The area of the cross section is 36π inch square, then the radius of the cylinder is 6 inches

If we slice a cylinder parallel to its base, we get a circle with the same radius as the cylinder.

We are given that the area of the cross section is 36π in square units. Since the cross section is a circle, we can use the formula for the area of a circle to find the radius.

The formula for the area of a circle is:

A = πr^2

where A is the area of the circle and r is the radius of the circle.

We are given that the area of the cross section is 36π. So, we can set A = 36π and solve for r:

36π = πr^2

Dividing both sides by π:

36 = r^2

Taking the square root of both sides:

r = ±6 inches

Since radius cannot be negative, the radius of the cylinder is 6 inches

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The equation has x = 2 and x = 5. A valid solution for x is x = 5

From the question, we have the following parameters that can be used in our computation:

√(x - 1) - 5 = x - 8

Add 5 to both sides

This gives

√(x - 1)  = x - 3

Square both sides

So, we have the following representation

x - 1 = x² - 6x + 9

Evaluate the like terms

x² - 7x + 10 = 0

This gives

(x - 2)(x - 5) = 0

Solve for x

x = 2 and x = 5

Testing the solutions, we have

√(2 - 1) - 5 = 2 - 8

-4 = -6 ---- falsee

√(5 - 1) - 5 = 5 - 8

-3 = -3 ---- true

Hene, the valid value of x is 5

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A correlation coefficient based on an observational study can only measure the strength of the relationship between two variables, and it cannot be used to prove a cause-and-effect relationship.

Even if the correlation is close to -1 or +1, this does not necessarily mean there is a cause-and-effect relationship between the two variables—it could be due to chance. Similarly, if the scatterplot of the data has little vertical variation, this does not necessarily mean there is a cause-and-effect relationship. The only way to prove a cause-and-effect relationship is through a controlled experiment. Therefore, the correlation coefficient based on an observational study can never be used to support a claim of cause and effect.

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There are 25 boys in the class out of a total of 40 students. The fraction of students who are boys is 5/8 and the fraction of students who are girls is 3/8.

Let's start by using the information given in the problem to determine the fraction of students who are girls in the class:

Fraction of students who are girls = 1 - Fraction of students who are boys

Fraction of students who are girls = 1 - 5/8

Fraction of students who are girls = 3/8

Now we can use the fraction of girls to find the number of boys and girls in the class:

Let the total number of students in the class be x.

Number of boys = 5/8 * x

Number of girls = 3/8 * x

We know that there are 15 girls in the class, so we can set up an equation:

3/8 * x = 15

Solving for x:

x = 15 * 8/3

x = 40

So there are 40 students in the class. Now we can find the number of boys:

Number of boys = 5/8 * x

Number of boys = 5/8 * 40

Number of boys = 25

Therefore, there are 25 boys in the class.

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Answer:

Two

Step-by-step explanation:

It's just- 1+1

Answer: 1 + 1 = 2

Step-by-step explanation:

The table given in the answer is an example of a conversion table that shows the decimal equivalents of powers of 16. The first row contains the values of 16 raised to the powers of 4, 3, 2, 1, and 0, respectively. The second row shows the equivalent decimal values of these powers of 16.                      

                                   16⁴      16³ 16² 16 1

                                  256 64 16 4 1

These values could also be expressed using radicals or rational numbers, but in this case, the decimal form is simpler and more commonly used.

This can be calculated as 16 x 16 x 16 x 16, which equals 65,536. Similarly, the second entry in the first row is 16³, which means 16 raised to the third power.

To understand why this is the case, we need to convert 16⁴ to decimal form. This can be done by multiplying each digit in the binary representation of 16⁴ by the corresponding power of 2 and adding up the results.

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Answer: the probability of being offered both jobs is 0.05, or 5%

Step-by-step explanation:

To solve this problem, we can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

where P(A or B) is the probability of getting at least one job offer, P(A) is the probability of getting an offer for job A, P(B) is the probability of getting an offer for job B, and P(A and B) is the probability of getting an offer for both jobs.

Substituting the given values, we get:

0.40 = 0.25 + 0.20 - P(A and B)

Solving for P(A and B), we get:

P(A and B) = 0.25 + 0.20 - 0.40 = 0.05

Therefore, the probability of being offered both jobs is 0.05, or 5% (rounded to two decimal places).

So the two ordered pairs that have a ratio of -4/3 are (-4, 3) and (4, -3).

where x and y are the first and second numbers in the ordered pair, respectively.

Checking each of the four given ordered pairs, we can see which ones satisfy this equation:

(-3, 4): -3/4 ≠ -4/3

(-4, 3): -4/3 = -4/3

(4, -3): 4/-3 = -4/3

(3, -4): 3/-4 ≠ -4/3

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We may use the formula 1Hp = 735Watt to convert watts to horsepower.

Watt and horsepower are both units of power.

But horsepower is a more powerful unit of power. We use horsepower to measure the power of electrical instruments such as turbines, motors, and a variety of other devices.

Thus, according to normal unit conversion rates, 1 Horsepower Equals 735 Watt.

1 Hp = 735 W

As a result, we have the conventional relationship 1Hp = 735 W. We may now simply convert any power supplied in horsepower to the unit of Watt.

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The length of arc FGE is given as follows:

230º.

The angle addition postulate states that if two angles share a common vertex and a common angle, forming a combination, the larger angle will be given by the sum of the smaller angles.

The entire circumference has an angle measure of 360º, while the arc EH has an angle measure of 130º, hence the length of arc FGE is obtained as follows:

x + 130 = 360

x = 360 - 130

x = 230º.

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Answer: x should be equal to 9 (please correct me if i'm wrong)

Step-by-step explanation: Let's say the answer for this problem is equal to x

4 -(-7) + (-2) = x

4 + 7 + (-2) = x

11 + (-2) = x

9 = x

Answer:

11/20

Step-by-step explanation:

3/4 - 1/5

= 15/20 - 4/20

= 11/20

So, the answer is 11/20

Answer:

The expected number of times Henry would remove a strawberry chew from the bag is about 1041. This can be calculated by multiplying the total number of trials (23 + 1300 = 1323) with the relative probability of each type of chew (17/23 = 0.7391 for strawberry, 3/23 = 0.1304 for lemon, 3/23 = 0.1304 for peach). The expected number of times Henry would remove a strawberry chew from the bag is 0.7391 x 1323 = 1041.24, which can be rounded to 1041.

Answer:

Step-by-step explanation

The answer is 961 . I can explain because, it is really easy all you have to do is add 17 and 23 together because it is only asking about strawberry so lower number on top and higher on bottom you get 17/23 then u put this equation 1300 times 17/23 you will get 960 and some decimals round up to 961 there you go you've got your anwser.